Problem $3$: Analysis and Deflection of Simple Frame

Consider the frame below which is fixed at A and pinned at E with a hinge at mid$-$span of the beam and column at D and B $,$ respectively. The flexural rigidity is constant for all members with $\backslash (\backslash$mathrm$\{$E$\}=\backslash )200$ GPa and $\backslash ($ I$=1200\backslash$times $10^\{6\}\backslash$mathrm$\{$~mm$\}4\backslash ).$ All reactions due to real loads are given.

a$.$ Analyze the frame and sketch the axial, shear, and moment diagrams. Indicate all critical points on all diagrams, including zero$-$crossings, points of inflection, and local minima$/$maxima$.$

b$.$ Sketch the qualitative deflected shape of the frame.

c$.$ Determine the vertical deflection of the hinge at D $($neglect axial deformation$).$